Suspended object moment of inertia

A 15.0 kg bucket of water is suspended by a very light rope wrapped around a solid cylinder 0.300 m in diameter with a mass of 12.0 kg. The cylinder pivots on a frictionless axle through its centre. The bucket is released from rest at the top of a well and falls 10.0 m to the water.
a) What is the tension in the rope while the bucket is falling?
b) With what speed does the bucket strike the water?
c) What is the time of the fall?
d) While the bucket is falling, what is the force exerted on the cylinder by the axle?

2. Relevant equations

T-Mg=ma
I=mr^2

3. The attempt at a solution
For a) i have solved as far as T-147.15=12a
how do i find a??

A 15.0 kg bucket of water is suspended by a very light rope wrapped around a solid cylinder 0.300 m in diameter with a mass of 12.0 kg. The cylinder pivots on a frictionless axle through its centre. The bucket is released from rest at the top of a well and falls 10.0 m to the water.
a) What is the tension in the rope while the bucket is falling?
b) With what speed does the bucket strike the water?
c) What is the time of the fall?
d) While the bucket is falling, what is the force exerted on the cylinder by the axle?

2. Relevant equations

T-Mg=ma
I=mr^2

3. The attempt at a solution
For a) i have solved as far as T-147.15=12a
how do i find a??

To calculate T, we have to consider torque acting on the cylinder due to the tension.
Torque τ = r*T = Iα = 1/2*Mr^2*α....(1)
The tangential acceleration a = r*α. so α = a/r.
Substitute this value in eq(1). find T.
From that find a.

ok so i think i know what everything is, small T is torque(we use tau) , big T is Tension.. so i tried to solve for a but using Ia/r=1/2mr^2a/r but the a's just cancel out. i cant use the T*r because i dont know the tension... Please help.

Hey thankyou that was very helpful, did you get a =7m/s^2 sound right to me - less than free fall... just to let you know the reason i was having so much trouble from your 1st post was that i had alpha=r/a not a/r

Hi, just a quick question. why do they give the radius of the cylinder if it is not needed, is there a way to solve these problems that does require the radius?
I have another very similar problem to this that i didnt use the radius for either.

Hey can you tell me how to do it if thats not right please, and about the radius? the thing that he said was F=ma was the force the axle exerts of the cylinder. Is the rest of my answers correct? you said that they looked good in my other post, sorry about the amount of posts but i really need the correct answers.

HEy just interested to know, i tried solving for the final velocity with the energy method you showed me(ehild) and it came out at about 9m/s but with kinematic equations using the found acceleration of 7m/s^2 it comes out to 11.8m/s. why would this be?

I haven't show you any method to get the final velocity. Maybe, it was somebody else in an other thread you started. Show your full work, how do you get the final velocity if a body moves 10 m with acceleration a=7 m/s^2 ?

i dont have any trouble with normal kinematics, v=sqrt(2*10*7) since u is 0. that comes out to 11.9. The other way i was trying was total energy initial-E=mgh+1/2mv^2+1/2Iw^2 and then letting w=v^2/r^2 and solving for v.... i think that i know why its not working, the bucket would still have some unknown mgh when it hits the water not 0?????
this is the one that i was talking about: https://www.physicsforums.com/showthread.php?t=399445

i dont have any trouble with normal kinematics, v=sqrt(2*10*7) since u is 0. that comes out to 11.9. The other way i was trying was total energy initial-E=mgh+1/2mv^2+1/2Iw^2 and then letting w=v^2/r^2 and solving for v.... i think that i know why its not working, the bucket would still have some unknown mgh when it hits the water not 0?????
this is the one that i was talking about: https://www.physicsforums.com/showthread.php?t=399445

If you set the surface of the water to h=0 then there will not be any remaining potential energy when the bucket hits the water.